二维和三维非自伴算子谱的数值计算方法
Numerical approaches to compute spectra of non-self adjoint operators in dimensions two and three
AI总结：
针对二维和三维空间中非自伴二次算子谱的数值计算问题，回顾一维相关结果后，提出有限差分离散化方法，解决非线性特征值问题并分析结果，延续了一维工作。
摘要：
本文关注二维和三维空间中非自伴二次算子谱的数值计算。实际上，在多维情况下，关于特征值位置的已知结果非常少，这导致需要求解非线性特征值问题。引言部分首先回顾了一维情况下已获得的理论结果和数值结果，然后介绍了为二维和三维情况开发的计算谱的数值方法（有限差分离散化），并展示和分析了得到的数值结果。此处的一个难点是必须计算强非自伴且不稳定的算子的特征值。本工作是之前一维空间工作的延续。
英文摘要：
In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the eignevalues. This leads to solve nonlinear eigenvalue problems. In introduction we begin with a review of theoretical results and numerical results obtained for the one dimensional case. Then we present the numerical methods developed to compute the spectra (finite difference discretization) for the two and three dimensional cases. The numerical results obtained are presented and analyzed. One difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are unstable. This work is in continuity of a previous work in one spatial dimension.
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